MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions

For what value of k, the function defined by

f(x) = `{{:((log(1 + 2x)sin^0)/x^2",", "for"  x ≠ 0),(k",", "for"  x = 0):}`

is continuous at x = 0 ?

The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))` respectively are ______.

Which of the following equation does not represent a pair of lines?

The value of sin 495° is ______.

The value of sin(– 1125°) is ______.

The value of `sin((25π)/3)` is ______.

The value of `cos((41π)/4)` is ______.

The value of `cos  π/8 + cos  (3π)/8 + cos  (5π)/8 + cos  (7π)/8` is ______.

The value of `2 cot^2(π/6) + 4 tan^2(π/6) - 3  "cosec"(π/6)` is ______.

Find the value of `cos ((29 π)/3)`.

If `cosA/3 = cosB/4 = 1/5, - π/2 < A < 0` and `- π/2 < B < 0`, then the value of 2 sin A + 4 sin B is ______.

The value of `(cot 54^circ)/(tan 36^circ) + (tan 20^circ)/(cot 70^circ)` is ______.

The value of cos 480° sin 150° + sin 600° cos 390° is ______.

The value of `cos^2  π/16 + cos^2  (3π)/16 + cos^2  (5π)/16 + cos^2  (7π)/16` is ______.

sin² 17.5° + sin² 72.5° is equal to ______.

If cos θ = `- sqrt(3)/2` and sin α = `-3/5`, where θ does not and α lies in the third quadrant, then `(2 tan α + sqrt(3) tan θ)/(cot^2 θ + cos alpha)` is equal to ______.

If tan θ = `1/sqrt(7)`, then `(("cosec"^2θ - sec^2θ))/(("cosec"^2θ + sec^2θ))` is equal to ______.

cos 1° + cos 2° + cos 3° + ... + cos 180° is equal to ______.

In a ΔABC, if ∠A = `π/2`, then cos² B + cos² C is equal to ______.

If ΔABC is a right angled at C, then tan A + tan B is equal to ______.